diff options
Diffstat (limited to 'Master/texmf-dist/tex')
-rw-r--r-- | Master/texmf-dist/tex/generic/pst-eucl/pst-eucl.tex | 685 |
1 files changed, 651 insertions, 34 deletions
diff --git a/Master/texmf-dist/tex/generic/pst-eucl/pst-eucl.tex b/Master/texmf-dist/tex/generic/pst-eucl/pst-eucl.tex index 8979b313bea..690515707d2 100644 --- a/Master/texmf-dist/tex/generic/pst-eucl/pst-eucl.tex +++ b/Master/texmf-dist/tex/generic/pst-eucl/pst-eucl.tex @@ -20,8 +20,8 @@ \csname PSTEuclideLoaded\endcsname \let\PSTEuclideLoaded\endinput % -\def\fileversion{1.66} -\def\filedate{2019/10/20} +\def\fileversion{1.67} +\def\filedate{2019/10/28} %% \message{`PST-Euclide v\fileversion, \filedate\space (dr,hv)}% %% prologue for postcript @@ -587,7 +587,6 @@ \def\pst@circle@node{#3} \@ifnextchar[\pstCircleOA@i{\pstCircleOA@i[0][360]}}% \def\pstCircleOA@i[#1][#2]{% - \rput(\pst@circle@center){% \begin@OpenObj \def\pst@linetype{4}% \addto@pscode{% @@ -605,7 +604,6 @@ #1 #2 arc}% \showpointsfalse \end@OpenObj - }% \endgroup% }% %% #2 #3 -> 2 nodes defining a diameter of the circle @@ -618,19 +616,17 @@ \@ifnextchar[\pstCircleAB@i{\pstCircleAB@i[0][360]}}% \def\pstCircleAB@i[#1][#2]{% \Pst@MiddleAB[PointSymbol=none, PointName=none]{\pst@circle@diameter@B}{\pst@circle@diameter@A}{PST@CIRCLE@MAB} - \rput(\pst@circle@diameter@A){% - \begin@OpenObj - \def\pst@linetype{4}% - \addto@pscode{% - tx@NodeDict begin - tx@NodeDict /N@PST@CIRCLE@MAB load GetCenter - end - 2 copy - tx@EcldDict begin /N@\pst@circle@diameter@B\space GetNode ABDist end - \psk@dimen\space CLW mul sub #1 #2 arc}% - \showpointsfalse - \end@OpenObj - }% + \begin@OpenObj + \def\pst@linetype{4}% + \addto@pscode{% + tx@NodeDict begin + tx@NodeDict /N@PST@CIRCLE@MAB load GetCenter + end + 2 copy + tx@EcldDict begin /N@\pst@circle@diameter@B\space GetNode ABDist end + \psk@dimen\space CLW mul sub #1 #2 arc}% + \showpointsfalse + \end@OpenObj \endgroup% }% %% #2 #3 #4 -> 3 nodes defining the center and two points on the circle @@ -1673,25 +1669,100 @@ }% % %% Distance between two points -\def\pstDistAB#1#2{% +\def\pstDist#1#2{% + tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode ABDist end +} +\def\pstDistAB#1#2{% Obsoleted tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode ABDist end \ifx\psk@DistCoef\@none\else \psk@DistCoef\space mul \fi } +% +% \pstDistMul{A}{B}{\lambda} -> \lambda * |AB| +%% Distance |AB| multiply with coefficient \lambda +\def\pstDistMul#1#2#3{% + tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode ABDist #3 mul end +} +% +% \pstDistAdd{A}{B}{C}{D} -> |AB| + |CD| +%% Distance sum of two segments AB and CD +\def\pstDistAdd#1#2#3#4{% + tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode ABDist + /N@#3 GetNode /N@#4 GetNode ABDist add end +} +% +% \pstDistAddVal{A}{B}{coef1}{val} -> |AB| * coef1 + val +\def\pstDistAddVal#1#2#3#4{% + tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode ABDist + #3 mul #4 add end +} +% +% \pstDistAddCoef{A}{B}{coef1}{C}{D}{coef2} -> |AB| * coef1 + |CD| * coef2 +\def\pstDistAddCoef#1#2#3#4#5#6{% + tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode ABDist + #3 mul /N@#4 GetNode /N@#5 GetNode ABDist #6 mul add end +} +% +%% Distance difference between two segments AB and CD +\def\pstDistSub#1#2#3#4{% + tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode ABDist + /N@#3 GetNode /N@#4 GetNode ABDist sub abs end +} +% +% \pstDistSubVal{A}{B}{coef1}{val} -> |AB| * coef1 - val +\def\pstDistSubVal#1#2#3#4{% + tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode ABDist + #3 mul #4 sub abs end +} +% +% \pstDistSubCoef{A}{B}{coef1}{C}{D}{coef2} -> |AB| * coef1 - |CD| * coef2 +\def\pstDistSubCoef#1#2#3#4#5#6{% + tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode ABDist + #3 mul /N@#4 GetNode /N@#5 GetNode ABDist #6 mul sub abs end +} +% +%% Distance ratio of two segments AB and CD +\def\pstDistDiv#1#2#3#4{% + tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode ABDist + /N@#3 GetNode /N@#4 GetNode ABDist div end +} +% %% Distance specified with a number -\def\pstDistVal#1{% - #1 \pst@number\psxunit mul +\def\pstDistConst#1{#1 \pst@number\psxunit mul\space} +\def\pstDistVal#1{% Obsoleted + #1 \pst@number\psxunit mul \ifx\psk@DistCoef\@none\else \psk@DistCoef\space mul \fi } -\def\pstDistCalc#1{% +\def\pstDistExpr#1{\pscalculate{#1} \pst@number\psxunit mul\space} +\def\pstDistCalc#1{% Obsoleted \pscalculate{#1} \pst@number\psxunit mul \ifx\psk@DistCoef\@none\else \psk@DistCoef\space mul \fi } +% +\def\pstDistCoef#1{#1 \ifx\psk@DistCoef\@none\else\psk@DistCoef\space mul\space\fi} +\def\pstUserDist#1{#1 \pst@number\psxunit div\space} +\def\pstScreenDist#1{#1 \pst@number\psxunit mul\space} +% +% \pstDistABC{A}{B}{C} -> return the distance from C to AB. +\def\pstDistABC#1#2#3{% + tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode /N@#3 GetNode + % x1 y1 x2 y2 x3 y3 + 5 index 5 index 5 index 5 index ABDist % |AB| + 6 index 6 index 4 index 4 index ABDist % |AC| + 5 index 5 index 5 index 5 index ABDist % |BC| + 2 index 2 index add 1 index add 2 div % p + 0 index 4 index sub % p-|AB| + 1 index 4 index sub % p-|AC| + 2 index 4 index sub % p-|BC| + mul mul mul sqrt 3 index div 2 mul + 10 1 roll pop pop pop pop pop pop pop pop pop end +} +% %% angle defined by three points \def\pstAngleAOB#1#2#3{% % \pstGeonode[PointName=none,PointSymbol=none](#1){temp@1}(#2){temp@2}(#3){temp@3}% @@ -1837,6 +1908,128 @@ \endgroup% }% % +%% \pstProportionNode[Options]{A}{B}{lambda}{C}{C'} +%% Create node C and C' which satisified the definite proportion function |AC|:|BC|=lamba, +%% where lambda is positive, C is inside segment AB, and C' is outside segment AB. +%% According to the definite proportion equation, we have +%% $$x_{C}=\dfrac{x_{A}+\lambda{}x_{B}}{1+\lambda},y_{C}=\dfrac{y_{A}+\lambda{}y_{B}}{1+\lambda}$$ +%% and +%% $$x_{C'}=\dfrac{x_{A}-\lambda{}x_{B}}{1-\lambda},y_{C'}=\dfrac{y_{A}+-lambda{}y_{B}}{1-\lambda}$$ +%% Parameters: +%% #1 -> options +%% #2 -> the given segment start node A +%% #3 -> the given segment end node B +%% #4 -> the definite proportion $\lambda$ +%% #5 -> the target node C inside segment AB +%% #6 -> the target node C' outside segment AB +\def\pstProportionNode{\@ifnextchar[\Pst@ProportionNode{\Pst@ProportionNode[]}} +\def\Pst@ProportionNode[#1]{% + \begingroup + \@InitListMng % + \psset{#1}% + \Pst@ProportionNode@i} +\def\Pst@ProportionNode@i#1#2#3#4#5{% + \pst@getcoor{#1}\pst@tempA% + \pst@getcoor{#2}\pst@tempB% + \pnode(! + \pst@tempA \tx@UserCoor % x1,y1 + \pst@tempB \tx@UserCoor % x2,y2 + #3 abs % \lambda + 4 index 1 index 4 index mul add 1 index 1 add div % (x1+\lambda*x2)/(1+\lambda) + 4 index 2 index 4 index mul add 2 index 1 add div % (y1+\lambda*y2)/(1+\lambda) + 7 2 roll pop pop pop pop pop + ){#4}% + \pnode(! + \pst@tempA \tx@UserCoor % x1,y1 + \pst@tempB \tx@UserCoor % x2,y2 + #3 abs % \lambda + dup 1 sub abs 1E-5 lt { + pop pop pop pop pop 0 0 + } { + 4 index 1 index 4 index mul sub 1 index 1 exch sub div % (x1-\lambda*x2)/(1-\lambda) + 4 index 2 index 4 index mul sub 2 index 1 exch sub div % (y1-\lambda*y2)/(1-\lambda) + 7 2 roll pop pop pop pop pop + } ifelse + ){#5}% + \Pst@ManageParamList{#4}% + \Pst@ManageParamList{#5}% + \endgroup% +}% +% +%% \pstFourthHarmonicNode[Options]{A}{B}{C}{D} +%% Create node D such that the four collinear points A,B,C,D form harmonic conjugate points, +%% that is, $(AB,CD)=\dfrac{AC}{BC}:\dfrac{AD}{BD}=-1$. +%% Parameters: +%% #1 -> options +%% #2 -> the given collinear base node A +%% #3 -> the given collinear base node B +%% #4 -> the given collinear proportion node C +%% #5 -> the output proportion node D +\def\pstFourthHarmonicNode{\@ifnextchar[\Pst@FourthHarmonicNode{\Pst@FourthHarmonicNode[]}} +\def\Pst@FourthHarmonicNode[#1]{% + \begingroup + \@InitListMng % + \psset{#1}% + \Pst@FourthHarmonicNode@i} +\def\Pst@FourthHarmonicNode@i#1#2#3#4{% + \pst@getcoor{#1}\pst@tempA% + \pst@getcoor{#2}\pst@tempB% + \pst@getcoor{#3}\pst@tempC% + \pnode(! + \pst@tempA \tx@UserCoor % x1,y1 + \pst@tempB \tx@UserCoor % x2,y2 + \pst@tempC \tx@UserCoor % x3,y3 + 5 index 4 index sub abs 1E-5 lt { % if x1=x2 + 5 index 2 index sub abs 1E-5 lt { % if x1=x3 + 4 index 1 index mul 3 index 2 index mul add 5 index 4 index mul 2 mul sub % y1y3+y2y3-2y1y2 + 1 index 2 mul 6 index sub 4 index sub % 2y3-y1-y2 + dup abs 1E-5 lt { + pop pop pop pop pop pop pop pop + 0 0 + } { + div % y=\dfrac{y1y3+y2y3-2y1y2}{2y3-y1-y2} + 2 index exch % x=x3 + 8 2 roll pop pop pop pop pop pop + } ifelse + } { + % C is not collinear with AB. + pop pop pop pop pop pop + 0 0 + } ifelse + } { + 5 index 2 index sub abs 1E-5 lt { % if x1=x3 + pop pop pop pop pop pop 0 0 + } { + 2 index 5 index sub 4 index 7 index sub div % k(AB)=\dfrac{y2-y1}{x2-x1} + 4 index 6 index mul 7 index 5 index mul sub 5 index 8 index sub div % d(AB)=\dfrac{x2y1-x1y2}{x2-x1} + 2 index 7 index sub 4 index 9 index sub div % k(AC)=\dfrac{y3-y1}{x3-x1} + 4 index 8 index mul 9 index 5 index mul sub 5 index 10 index sub div % d(AC)=\dfrac{x3y1-x1y3}{x3-x1} + 3 index 2 index sub abs 1E-5 lt 3 index 2 index sub abs 1E-5 lt and { % k(AB)=k(AC) and d(AB)=d(AC) + % x=\dfrac{x1x3+x2x3-2x1x2}{2x3-x1-x2}; y=k(AC)x+d(AC) + 9 index 6 index mul 8 index 7 index mul add 10 index 9 index mul 2 mul sub + 6 index 2 mul 11 index sub 9 index sub + dup abs 1E-5 lt { + pop pop pop pop pop pop + pop pop pop pop pop pop + 0 0 + } { + div + 2 index 1 index mul 2 index add + 12 2 roll pop pop pop pop pop + pop pop pop pop pop + } ifelse + } { + % C is not collinear with AB. + pop pop pop pop pop pop pop pop + 0 0 + } ifelse + } ifelse + } ifelse + ){#4}% + \Pst@ManageParamList{#4}% + \endgroup% +}% +% %% \pstLine[Options]{node}{node} %% \pstLine[Options]{node}(coor) %% \pstLine[Options](coor){node} @@ -1960,6 +2153,184 @@ \endgroup% }% % +%% \pstLocateAB[Options]{A}{B}{distance}{C} +%% Locate node C on segment AB such that |AC|=distance, then create node C. +%% Note that locate C on BA will get the node C in the reverse order. +%% Parameters: +%% #1 -> options +%% #2 -> the given segment start node A +%% #3 -> the given segment end node B +%% #4 -> the specified length in screen coordinate +%% #5 -> the target node C +\def\pstLocateAB{\@ifnextchar[\Pst@LocateAB{\Pst@LocateAB[]}} +\def\Pst@LocateAB[#1]{% + \begingroup + \psset{#1}% + \Pst@LocateAB@i} +\def\Pst@LocateAB@i#1#2#3#4{% + \pst@getcoor{#1}\pst@tempA% + \pst@getcoor{#2}\pst@tempB% + \pnode(! + \pst@tempA \tx@UserCoor % x1,y1 + \pst@tempB \tx@UserCoor % x2,y2 + #3 abs \pst@number\psxunit div % User distance + 4 index 3 index sub abs 1E-5 lt { % if x1=x2 + 3 index 2 index lt { % if y1 < y2 + 3 index 1 index add % y1 + l + } { + 3 index 1 index sub % y1 - l + } ifelse + 3 index exch + 7 2 roll pop pop pop pop pop + } { + 1 index 4 index sub 3 index 6 index sub div % k = (y2-y1)/(x2-x1) + 1 index 1 index dup mul 1 add sqrt div % l/sqrt(k^2+1) + 4 index 7 index lt { % if x2<x1 + 6 index exch sub % x1 - l/sqrt(k^2+1) + } { + 6 index add % x1 + l/sqrt(k^2+1) + } ifelse + 3 index 1 index 6 index sub 3 index mul add % y = y2+(x-x2)k + 8 2 roll pop pop pop pop pop pop + } ifelse + ){#4}% + \Pst@geonodelabel{#4}% + \endgroup% +}% +% +%% \pstLabelAB[Options]{A}{B}{label} +%% Print the label for segment AB. +%% Options: +%% - linestyle: the line style to control the ruler bar +%% - arrows: the line arrows to control the ruler bar +%% - offset: the seperation between label and segment +%% - nrot: the rotation of the label +%% - npos: the proportion of the label +\def\pstLabelAB{\@ifnextchar[\Pst@LabelAB{\Pst@LabelAB[]}} +\def\Pst@LabelAB[#1]#2#3#4{% + \begingroup + \psset{linestyle=none} % default not show the rule bar. + \psset{offset=10pt} % default offset is 10pt + \psset{nrot=:U} % default rotation is :U + \psset{npos=0.5} % default label proportion from A to B is 0.5 + \psset{#1}\ncline{#2}{#3}\ncput*{#4} + \endgroup% +}% +%% \pstExtendAB[Options]{A}{B}{distance}{C} +%% Extend AB to C such that |BC|=distance, then create node C. +%% Note that extend BA to C will get the node C in the reverse order. +%% Parameters: +%% #1 -> options +%% #2 -> the given segment start node A +%% #3 -> the given segment end node B +%% #4 -> the specified length in screen coordinate +%% #5 -> the target node C +\def\pstExtendAB{\@ifnextchar[\Pst@ExtendAB{\Pst@ExtendAB[]}} +\def\Pst@ExtendAB[#1]{% + \begingroup + \psset{#1}% + \Pst@ExtendAB@i} +\def\Pst@ExtendAB@i#1#2#3#4{% + \pst@getcoor{#1}\pst@tempA% + \pst@getcoor{#2}\pst@tempB% + \pnode(! + \pst@tempA \tx@UserCoor % x1,y1 + \pst@tempB \tx@UserCoor % x2,y2 + #3 abs \pst@number\psxunit div % User distance + 4 index 3 index sub abs 1E-5 lt { % if x1=x2 + 3 index 2 index lt { % if y1 < y2 + 1 index 1 index add % y2 + l + } { + 1 index 1 index sub % y2 - l + } ifelse + 3 index exch + 7 2 roll pop pop pop pop pop + } { + 1 index 4 index sub 3 index 6 index sub div % k = (y2-y1)/(x2-x1) + 1 index 1 index dup mul 1 add sqrt div % l/sqrt(k^2+1) + 4 index 7 index lt { % if x2<x1 + 4 index exch sub % x2 - l/sqrt(k^2+1) + } { + 4 index add % x2 + l/sqrt(k^2+1) + } ifelse + 3 index 1 index 6 index sub 3 index mul add % y = y2+(x-x2)k + 8 2 roll pop pop pop pop pop pop + } ifelse + ){#4}% + \Pst@geonodelabel{#4}% + \endgroup% +}% +% +%% \pstInversion[Options]{O}{A}{C}{C'} +%% Find the inversion point $C'$ of $C$ such that $|OC|*|OC'|=|OA|^2$, then create node $C'$. +%% We call $O$ as the inversion center, and |OA| as the inversion radius. +%% Parameters: +%% #1 -> options +%% #2 -> the inversion center O +%% #3 -> the inversion radius OA, or the specified Radius/Diameter if empty +%% #4 -> the initial node C +%% #5 -> the target node C' +\def\pstInversion{\@ifnextchar[\Pst@Inversion{\Pst@Inversion[]}} +\def\Pst@Inversion[#1]{% + \begingroup + \psset{#1}% + \Pst@Inversion@i} +\def\Pst@Inversion@i#1#2#3#4{% + \pstLocateAB{#1}{#3}{% + tx@EcldDict begin /N@#1 GetNode /N@#3 GetNode ABDist end % |OC| + % use Radius or Diameter to get the inversion radius. + \ifx\psk@Radius\@none + \ifx\psk@Diameter\@none + tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode ABDist end + \else + \psk@Diameter\space 2 div + \fi + \else + \psk@Radius\space + \fi + dup mul exch div % |OA|^2/|OC| + }{#4} + \endgroup% +}% +% +%% \pstGeometricMean[Options]{A}{B}{l1}{l2}{C} +%% Find the point $C$ on segment AB such that $|AC|^2=l_1*l_2$, then create node $C$. +%% Parameters: +%% #1 -> options +%% #2 -> the first node A on the given segment +%% #3 -> the second node B on the given segment +%% #4 -> the given segment length l1 +%% #5 -> the given segment length l2 +%% #6 -> the target node C +\def\pstGeometricMean{\@ifnextchar[\Pst@GeometricMean{\Pst@GeometricMean[]}} +\def\Pst@GeometricMean[#1]{% + \begingroup + \psset{#1}% + \Pst@GeometricMean@i} +\def\Pst@GeometricMean@i#1#2#3#4#5{% + \pstLocateAB{#1}{#2}{#3 #4 mul sqrt}{#5} + \endgroup% +}% +% +%% \pstHarmonicMean[Options]{A}{B}{l1}{l2}{C} +%% Find the point $C$ on segment AB such that $1/|AC|=(1/l_1+1/l_2)/2$, then create node $C$. +%% Parameters: +%% #1 -> options +%% #2 -> the first node A on the given segment +%% #3 -> the second node B on the given segment +%% #4 -> the given segment length l1 +%% #5 -> the given segment length l2 +%% #6 -> the target node C +\def\pstHarmonicMean{\@ifnextchar[\Pst@HarmonicMean{\Pst@HarmonicMean[]}} +\def\Pst@HarmonicMean[#1]{% + \begingroup + \psset{#1}% + \Pst@HarmonicMean@i} +\def\Pst@HarmonicMean@i#1#2#3#4#5{% + \pstLocateAB{#1}{#2}{#3 #4 2 copy mul 3 1 roll add div 2 mul}{#5} + \endgroup% +}% +% %% \pstCircleAbsNode[Options]{O}{A}{$x_0$}{C}{D} %% Create the new nodes C and D on the Circle O whose abscissas are the given value $x_0$. %% The circle O is defined by center O and point A on the circle or Radius in parameter. @@ -2006,6 +2377,40 @@ \endgroup% }% % +%% \pstCircleNode[Options]{O}{A}{anglge}{X} +%% Create a new node X on the Circle O whose angle is the given value. +%% The circle O is defined by center O and point A on the circle or Radius in parameter. +%% Parameters: +%% #1 -> options +%% #2 -> [input] the circle center O +%% #3 -> [input] the circle point A or empty with Radius parameter +%% #4 -> [input] the input angle value +%% #4 -> [output] the target node name +\def\pstCircleNode{\@ifnextchar[\Pst@CircleNode{\Pst@CircleNode[]}} +\def\Pst@CircleNode[#1]{% + \begingroup + \psset{#1}% + \Pst@CircleNode@i} +\def\Pst@CircleNode@i#1#2#3#4{% + \pnode(! + tx@EcldDict begin + /N@#1 GetNode + \ifx\psk@Radius\@none + \ifx\psk@Diameter\@none + 2 copy /N@#2 GetNode ABDist + \else\psk@Diameter 2 div + \fi + \else\psk@Radius\space + \fi + end + #3 dup sin exch cos + 2 index mul 4 index add \pst@number\psxunit\space div % + 5 1 roll mul add \pst@number\psyunit\space div exch pop% + ){#4}% + \Pst@geonodelabel{#4}% + \endgroup% +}% +% %% \pstCircleRotNode[Options]{O}{A}{X} %% Create a new node X on the Circle O whose RotAngle is the given value. %% The circle O is defined by center O and point A on the circle or Radius in parameter. @@ -2032,7 +2437,7 @@ \else\psk@Radius\space \fi end - \psk@RotAngle\space sin \psk@RotAngle\space cos % + \psk@RotAngle\space dup sin exch cos % 2 index mul 4 index add \pst@number\psxunit\space div % 5 1 roll mul add \pst@number\psyunit\space div exch pop% ){#3}% @@ -2181,18 +2586,21 @@ %% The circle B(O1) is defined by center O2 and point B on the circle or RadiusB/DiameterB in parameter. %% Parameters: %% #1 -> options -%% #2 -> [input] the circle center O -%% #3 -> [input] the circle point A or empty with Radius parameter -%% #4 -> [input] the node name T out of circle -%% #5 -> [output] the first target name on the circle -%% #6 -> [output] the second target name on the circle +%% #2 -> [input] the first circle center O1 +%% #3 -> [input] the first circle point A or empty with RadiusA/DiameterA parameter +%% #4 -> [input] the second circle center O2 +%% #5 -> [input] the second circle point B or empty with RadiusB/DiameterB parameter +%% #6 -> [output] the first node name T1 lies on circle A(O1) +%% #7 -> [output] the second node name T2 lies on circle A(O1) +%% #8 -> [output] the first node name T3 lies on circle B(O2) +%% #9 -> [output] the second node name T4 lies on circle B(O2) \def\pstCircleExternalCommonTangent{\@ifnextchar[\Pst@CircleExternalCommonTangent{\Pst@CircleExternalCommonTangent[]}} \def\Pst@CircleExternalCommonTangent[#1]{% \begingroup \@InitListMng % \psset{#1}% - \Pst@CircleExternCommonTangent@i} -\def\Pst@CircleExternCommonTangent@i#1#2#3#4#5#6#7#8{% + \Pst@CircleExternalCommonTangent@i} +\def\Pst@CircleExternalCommonTangent@i#1#2#3#4#5#6#7#8{% % use edef to save the second Radius or Diameter. \edef\pst@RadiusB@temp{\psk@RadiusB} \edef\pst@DiameterB@temp{\psk@DiameterB} @@ -2262,11 +2670,14 @@ %% The circle B(O1) is defined by center O2 and point B on the circle or RadiusB/DiameterB in parameter. %% Parameters: %% #1 -> options -%% #2 -> [input] the circle center O -%% #3 -> [input] the circle point A or empty with Radius parameter -%% #4 -> [input] the node name T out of circle -%% #5 -> [output] the first target name on the circle -%% #6 -> [output] the second target name on the circle +%% #2 -> [input] the first circle center O1 +%% #3 -> [input] the first circle point A or empty with RadiusA/DiameterA parameter +%% #4 -> [input] the second circle center O2 +%% #5 -> [input] the second circle point B or empty with RadiusB/DiameterB parameter +%% #6 -> [output] the first node name T1 lies on circle A(O1) +%% #7 -> [output] the second node name T2 lies on circle A(O1) +%% #8 -> [output] the first node name T3 lies on circle B(O2) +%% #9 -> [output] the second node name T4 lies on circle B(O2) \def\pstCircleInternalCommonTangent{\@ifnextchar[\Pst@CircleInternalCommonTangent{\Pst@CircleInternalCommonTangent[]}} \def\Pst@CircleInternalCommonTangent[#1]{% \begingroup @@ -2336,6 +2747,212 @@ \endgroup% }% % +%% \pstCircleRadicalAxis[Options]{O1}{A}{O2}{B}{C}{D} +%% Draw the radical axis of the circle A(O1) and B(O2), and create two nodes $C$ and $D$ on the axis. +%% The circle A(O1) is defined by center O1 and point A on the circle or RadiusA/DiameterA in parameter. +%% The circle B(O1) is defined by center O2 and point B on the circle or RadiusB/DiameterB in parameter. +%% For any point P(x,y) on the radical axis, we have +%% $$(x-x_1)^2+(y-y_1)^2-r_1^2=(x-x_2)^2+(y-y_2)^2-r_2^2$$ +%% case 1. when $x_1=x_2$, we have +%% $$2(y_2-y_1)y+y_1^2-r_1^2=y_2^2-r_2^2$$ +%% case 1.1. when $y_1=y_2$, there is none radical axis. +%% case 1.2. else we have +%% $$y=\dfrac{(y_2^2-r_2^2)-(y_1^2-r_1^2)}{2(y_2-y_1)}$$ +%% case 1.2.1. when $r_1^2-(y-y_1)^2<0$, there is none intersection of two circle, we select $x=x_1$ and $x=x_1+1$ at this time. +%% case 1.2.2. else we select $x=x_1\pm\sqrt{r_1^2-(y-y_1)^2}$ +%% case 2. when $x_1\neq{}x_2$, we have +%% case 2.1. when $y_1=y_2$, we have +%% $$x=\dfrac{(x_2^2-r_2^2)-(x_1^2-r_1^2)}{2(x_2-x_1)}$$ +%% case 2.1.1. when $r_1^2-(x-x_1)^2<0$, there is none intersection of two circle, we select $y=y_1$ and $y=y_1+1$ at this time. +%% case 2.1.2. else we select $y=y_1\pm\sqrt{r_1^2-(x-x_1)^2}$ +%% case 2.2. else we have +%% $$2(x_2-x_1)x+2(y_2-y_1)y=(x_2^2+y_2^2-r_2^2)-(x_1^2+y_1^2-r_1^2)$$ +%% set $a=2(x_2-x_1)$,$b=2(y_2-y_1)$,$m=x_2^2+y_2^2-r_2^2$,$n=x_1^2+y_1^2-r_1^2$, $d=m-n$,we have +%% $$ax+by=d$$ +%% when $(x-x_1)^2+(y-y_1)^2-r_1^2=0$, let $X=x-x_1$, $Y=y-y_1$, we have +%% $$X^2+Y^2=r_1^2$$ +%% and +%% $$aX+bY=d-ax_1-by_1$$ +%% let $e=d-ax_1-by_1$, then +%% $$(a^2+b^2)X^2-2aeX+e^2-b^2r_1^2=0$$ +%% case 2.2.1 when $(a^2+b^2)r_1^2-e^2>0$, we have +%% $$x=x_1+\dfrac{ae\pm{}b\sqrt{(a^2+b^2)r_1^2-e^2}}{a^2+b^2}$$ +%% $$y=y_1+\dfrac{be\mp{}a\sqrt{(a^2+b^2)r_1^2-e^2}}{a^2+b^2}$$ +%% case 2.2.2 else we select $x=\dfrac{r_1x_1+r_2x_2}{r_1+r_2}$ and $x=\dfrac{r_2x_1+r_1x_2}{r_1+r_2}$. +%% Parameters: +%% #1 -> options +%% #2 -> [input] the first circle center O1 +%% #3 -> [input] the first circle point A or empty with RadiusA/DiameterA parameter +%% #4 -> [input] the second circle center O2 +%% #5 -> [input] the second circle point B or empty with RadiusB/DiameterB parameter +%% #6 -> [output] the first node name C lies on radical axis +%% #7 -> [output] the second node name D lies on radical axis +\def\pstCircleRadicalAxis{\@ifnextchar[\Pst@CircleRadicalAxis{\Pst@CircleRadicalAxis[]}} +\def\Pst@CircleRadicalAxis[#1]{% + \begingroup + \@InitListMng % + \psset{#1}% + \Pst@CircleRadicalAxis@i} +\def\Pst@CircleRadicalAxis@i#1#2#3#4#5#6{% + \pst@getcoor{#1}\pst@tempA% + \pst@getcoor{#3}\pst@tempB% + \pnode(! + \pst@tempA \tx@UserCoor % x1,y1 + \pst@tempB \tx@UserCoor % x2,y2 + \ifx\psk@RadiusA\@undef + \ifx\psk@DiameterA\@undef + tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode ABDist end + \else + \psk@DiameterA\space 2 div + \fi + \else\psk@RadiusA\space\fi + \pst@number\psxunit div %r1 + \ifx\psk@RadiusB\@undef + \ifx\psk@DiameterB\@undef + tx@EcldDict begin /N@#3 GetNode /N@#4 GetNode ABDist end + \else + \psk@DiameterB\space 2 div + \fi + \else\psk@RadiusB\space\fi + \pst@number\psxunit div %r2 + 5 index 4 index sub abs 1E-5 lt { % if x1=x2 + 4 index 3 index sub abs 1E-5 lt { % if y1=y2 + pop pop pop pop pop pop 0 0 + } { + % x1 y1 x2 y2 r1 r2 + 2 index dup mul 1 index dup mul sub % y2^2-r2^2 + 5 index dup mul 3 index dup mul sub % y1^2-r1^2 + sub 3 index 6 index sub 2 mul div % y=\dfrac{(y2^2-r2^2)-(y1^2-r1^2)}{2(y2-y1)} + 6 index 3 index dup mul 2 index 8 index sub dup mul sub + dup 0 lt { + pop % x=x1 + } { + sqrt sub % x=x1\pm\sqrt{r1^2-(y-y1)^2)} + } ifelse + exch 8 2 roll pop pop pop pop pop pop + } ifelse + } { + 4 index 3 index sub abs 1E-5 lt { % if y1=y2 + % x1 y1 x2 y2 r1 r2 + 3 index dup mul 1 index dup mul sub % x2^2-r2^2 + 6 index dup mul 3 index dup mul sub % x1^2-r1^2 + sub 4 index 7 index sub 2 mul div % x=\dfrac{(x2^2-r2^2)-(x1^2-r1^2)}{2(x2-x1)} + 5 index 3 index dup mul 2 index 9 index sub dup mul sub + dup 0 lt { + pop % y=y1 + } { + sqrt sub % y=y1\pm\sqrt{r1^2-(x-x1)^2)} + } ifelse + 8 2 roll pop pop pop pop pop pop + } { + % x1 y1 x2 y2 r1 r2 + 3 index dup mul 3 index dup mul add 1 index dup mul sub % m=x2^2+y2^2-r2^2 + 6 index dup mul 6 index dup mul add 3 index dup mul sub % n=x1^2+y1^2-r1^2 + 1 index 1 index sub % d=m-n + 6 index 9 index sub 2 mul % a=2(x2-x1) + 6 index 9 index sub 2 mul % b=2(y2-y1) + 2 index 2 index 12 index mul sub 1 index 11 index mul sub % e=d-ax1-by1 + 2 index dup mul 2 index dup mul add 8 index dup mul mul 1 index dup mul sub % f=(a^2+b^2)r1^2-e^2 + dup 0 lt { + % we select x=\dfrac{r1x1+r2x2}{r1+r2} + 8 index 13 index mul 8 index 12 index mul add 9 index 9 index add div % x + % y=\dfrac{d-ax}{b} + 5 index 5 index 2 index mul sub 4 index div + 15 2 roll pop pop pop pop pop pop pop + pop pop pop pop pop pop + } { + sqrt % sqrt(f) + % x=x_1+\dfrac{ae\pm{}b\sqrt{(a^2+b^2)r_1^2-e^2}}{a^2+b^2} + 0 index 3 index mul 4 index 3 index mul exch sub 4 index dup mul 4 index dup mul add div 13 index add + % y=y_1+\dfrac{be\mp{}a\sqrt{(a^2+b^2)r_1^2-e^2}}{a^2+b^2} + 1 index 5 index mul 4 index 4 index mul add 5 index dup mul 5 index dup mul add div 13 index add + 15 2 roll pop pop pop pop pop pop + pop pop pop pop pop pop pop + } ifelse + } ifelse + } ifelse + ){#5} + \pnode(! + \pst@tempA \tx@UserCoor % x1,y1 + \pst@tempB \tx@UserCoor % x2,y2 + \ifx\psk@RadiusA\@undef + \ifx\psk@DiameterA\@undef + tx@EcldDict begin /N@#1 GetNode /N@#2 GetNode ABDist end + \else + \psk@DiameterA\space 2 div + \fi + \else\psk@RadiusA\space\fi + \pst@number\psxunit div %r1 + \ifx\psk@RadiusB\@undef + \ifx\psk@DiameterB\@undef + tx@EcldDict begin /N@#3 GetNode /N@#4 GetNode ABDist end + \else + \psk@DiameterB\space 2 div + \fi + \else\psk@RadiusB\space\fi + \pst@number\psxunit div %r2 + 5 index 4 index sub abs 1E-5 lt { % if x1=x2 + 4 index 3 index sub abs 1E-5 lt { % if y1=y2 + pop pop pop pop pop pop 0 0 + } { + % x1 y1 x2 y2 r1 r2 + 2 index dup mul 1 index dup mul sub % y2^2-r2^2 + 5 index dup mul 3 index dup mul sub % y1^2-r1^2 + sub 3 index 6 index sub 2 mul div % y=\dfrac{(y2^2-r2^2)-(y1^2-r1^2)}{2(y2-y1)} + 6 index 3 index dup mul 2 index 8 index sub dup mul sub + dup 0 lt { + pop 1 add % x=x1+1 + } { + sqrt add % x=x1\pm\sqrt{r1^2-(y-y1)^2)} + } ifelse + exch 8 2 roll pop pop pop pop pop pop + } ifelse + } { + 4 index 3 index sub abs 1E-5 lt { % if y1=y2 + 3 index dup mul 1 index dup mul sub % x2^2-r2^2 + 6 index dup mul 3 index dup mul sub % x1^2-r1^2 + sub 4 index 7 index sub 2 mul div % x=\dfrac{(x2^2-r2^2)-(x1^2-r1^2)}{2(x2-x1)} + 5 index 3 index dup mul 2 index 9 index sub dup mul sub + dup 0 lt { + pop 1 add % y=y1+1 + } { + sqrt add % y=y1\pm\sqrt{r1^2-(x-x1)^2)} + } ifelse + 8 2 roll pop pop pop pop pop pop + } { + % x1 y1 x2 y2 r1 r2 + 3 index dup mul 3 index dup mul add 1 index dup mul sub % m=x2^2+y2^2-r2^2 + 6 index dup mul 6 index dup mul add 3 index dup mul sub % n=x1^2+y1^2-r1^2 + 1 index 1 index sub % d=m-n + 6 index 9 index sub 2 mul % a=2(x2-x1) + 6 index 9 index sub 2 mul % b=2(y2-y1) + 2 index 2 index 12 index mul sub 1 index 11 index mul sub % e=d-ax1-by1 + 2 index dup mul 2 index dup mul add 8 index dup mul mul 1 index dup mul sub % f=(a^2+b^2)r1^2-e^2 + dup 0 lt { + % we select x=\dfrac{r2x1+r1x2}{r1+r2} + 7 index 13 index mul 9 index 12 index mul add 9 index 9 index add div % x + % y=\dfrac{d-ax}{b} + 5 index 5 index 2 index mul sub 4 index div + 15 2 roll pop pop pop pop pop pop pop + pop pop pop pop pop pop + } { + sqrt % sqrt(f) + % x=x_1+\dfrac{ae\pm{}b\sqrt{(a^2+b^2)r_1^2-e^2}}{a^2+b^2} + 0 index 3 index mul 4 index 3 index mul add 4 index dup mul 4 index dup mul add div 13 index add + % y=y_1+\dfrac{be\mp{}a\sqrt{(a^2+b^2)r_1^2-e^2}}{a^2+b^2} + 1 index 5 index mul 4 index 4 index mul exch sub 5 index dup mul 5 index dup mul add div 13 index add + 15 2 roll pop pop pop pop pop pop + pop pop pop pop pop pop pop + } ifelse + } ifelse + } ifelse + ){#6} + \Pst@ManageParamList{#5}% + \Pst@ManageParamList{#6}% + \pstLineAB{#5}{#6}% + \endgroup% +}% +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Here are some functions to operate the conic curves. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |